Warp

Apply projective or affine transformation

• 

Libraries:
Computer Vision Toolbox / Geometric Transformations

Description

The Warp block transforms an image by applying projective or affine transformation. You can transform the entire image or a region of the image by defining a rectangular region of interest (ROI).

Examples

Apply Horizontal Shear Transformation to Image

Read an image into the MATLAB workspace.

• Open Script

Rotate ROI in Image

Apply rotation transformation to a region of interest (ROI) in the input image.

• Open Script

Ports

Input

Image — Input image

matrix | 3-D numeric array

Input image, specified as one of these values:

• matrix — For intensity images of size M-by-N.

• 3-D numeric array — For true color images of size M-by-N-by-3.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

TForm — Transformation matrix

3-by-2 matrix | 3-by-3 matrix

Transformation matrix, specified as any one of these values:

• 3-by-2 matrix — For affine transformation.

• 3-by-3 matrix — For projective transformation.

For more information about the transformations, see Algorithms.

Dependencies

To enable this input port, set the Transformation matrix source parameter value to Input port.

Data Types: double | single

ROI — Region of interest

4-element vector

Region of interest, specified as a 4-element vector of form [x_s y_s width height]. x_s and y_s are the x and y coordinates of the top left corner of the ROI, respectively.

If you specify the ROI input, the Warp block applies transformation only to the specified region and returns the transformed region at the output.

Dependencies

To enable this input port, select the Enable ROI input port parameter.

Output

Image — Transformed image

matrix | 3-D numeric array

Transformed image, returned as one of these values:

• matrix — If input is an intensity image of size P-by-Q1.

• 3-D numeric array — If input is a true color image of size P-by-Q-by-3.

The data type of the output transformed image is same as that of the input image. The size of the output transformed image is either same as the input image or equal to the value set for the Output image position vector [x y width height] parameter.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Err_roi — Indicator for transformed ROI outside image region

0 | 1

Indicator for transformed ROI outside image region, returned as 0 or 1.

Data Types: Boolean

Parameters

Transformation matrix for source — Source for passing transformation matrix

Input port (default) | Custom

Source for passing transformation matrix, specified as either Input port or Custom. If you select Custom, you can enter the transformation matrix coefficients by using the Transformation matrix parameter that appears with this selection.

Transformation matrix — Value for transformation matrix

3-by-2 matrix | 3-by-3 matrix

Value for transformation matrix, specified as a 3-by-2 matrix for affine transformation or 3-by-3 matrix for projective transformation.

Dependencies

To enable this parameter, set the Transformation matrix for source parameter value to Custom.

Interpolation method — Method for interpolating transformed pixel values

Bilinear (default) | Nearest neighbor | Bicubic

Method for interpolating transformed pixel values, specified as Nearest neighbor, Bilinear, or Bicubic.

If you select Nearest neighbor, the block uses the value of an nearby pixel for the new pixel value. If you select Bilinear, the new pixel value is the weighted average of the four nearest pixel values. If you select Bicubic, the new pixel value is the weighted average of the sixteen nearest pixel values.

The number of pixels the block considers affects the complexity of the computation. Therefore, the Nearest neighbor interpolation is the most computationally efficient. However, because the accuracy of the method is proportional to the number of pixels considered, the Bicubic method is the most accurate. For information about the interpolation methods, see the More About section.

Background fill value — Intensity value for background pixels in the transformed image

0 (default) | scalar | 3-element vector

Intensity value for background pixels in the transformed image, specified as one of these values:

• scalar — If input image is a gray scale image.

• 3-element vector — If input image is a true color image. The vector is of the form [r g b] specifying the red (r), green (g), and blue (b) color channel values for the background pixels.

The default fill value is 0 and sets the background color to black.

Output image position source — Source for passing output image size

Same as input image (default) | Custom

Source for passing a value for the output image size, specified as either Same as input image or Custom.

• If you select Same as input image, the output transformed image is of same size as that of the input image.

• If you select Custom, you must specify a bounding box to output only the image region that lies within the bounding box. This selection enables the Output image position vector [x y width height] parameter that you can use for specifying the bounding box value.

Output image position vector [x y width height] — Size of the output image

[1 1 512 512] (default) | 4-element vector

Size of the output image, specified as a four element vector of form [x y width height]. When you specify this parameter, the Warp block creates a bounding box of specified width and height values. The size of the output image is set to the size of the bounding box and will contain the transformed image region that lies within the bounding box. If the size of the output image is greater than the size of the transformed image region within the bounding box, the intensity value of the extraneous pixels in the output image are set to the value specified for Background fill value parameter.

x and y are the spatial coordinates that define top-left corner position of the bounding box with respect to the input image.

Dependencies

To enable this parameter, set the Output image position source parameter value to Custom.

Enable ROI input port — Input ROI

off (default) | on

Select this parameter to enable the ROI input port and specify the ROI to be transformed.

Enable output port indicating if any part of ROI is outside input image — Output if transformed ROI is outside the specified image size

off (default) | on

Select this parameter to enable the Err_roi output port.

Dependencies

To enable this parameter, select the Enable ROI input port parameter.

Simulate using — Block simulation method

Interpreted Execution (default) | Code Generation

Block simulation method, specified as Interpreted Execution or Code Generation. If you want your block to use the MATLAB^® interpreter, choose Interpreted Execution. If you want your block to run as compiled code, choose Code Generation. For more information, see Choosing a Simulation Mode (Simulink).

Block Characteristics

Data Types	Boolean | double | fixed point | integer | single
Multidimensional Signals	yes
Variable-Size Signals	yes

More About

Nearest Neighbor Interpolation

For nearest neighbor interpolation, the block uses nearby, translated, pixel values for the output pixel values.

For example, suppose this matrix, represents your input image,

$$\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}$$

and you want to translate this image 1.7 pixels in the positive horizontal direction using nearest neighbor interpolation. These steps illustrate the nearest neighbor interpolation algorithm followed by the block:

1. Zero pad the input matrix and translate it 1.7 pixels to the right.

   

2. Create the output matrix by replacing each input pixel value with the translated value nearest to it resulting in this matrix:

   $$\begin{array}{ccccc}0& 0& 1& 2& 3\\ 0& 0& 4& 5& 6\\ 0& 0& 7& 8& 9\end{array}$$

Note

Despite specifying a value of 1.7 pixels to translate the image, this method translates the image by 2 pixels. Nearest neighbor interpolation is computationally efficient, but not as accurate as the bilinear and bicubic interpolation methods.

Bilinear Interpolation

For bilinear interpolation, the block uses the weighted average of two translated pixel values for each output pixel value.

For example, suppose this matrix, represents your input image,

$$\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}$$

and you want to translate this image by 0.5 pixels in the positive horizontal direction using bilinear interpolation. These steps illustrate the bilinear interpolation algorithm followed by the block:

1. Zero pad the input matrix and translate it 0.5 pixels to the right.

   

2. Create the output matrix by replacing each input pixel value with the weighted average of the translated pixel values on either side of the input pixel. The result is this matrix which has one column more than the input matrix.

   $$\begin{array}{cccc}0.5& 1.5& 2.5& 1.5\\ 2& 4.5& 5.5& 3\\ 3.5& 7.5& 8.5& 4.5\end{array}$$

Bicubic Interpolation

For bicubic interpolation, the block uses the weighted average of four translated pixel values for each output pixel value.

For example, suppose this matrix, represents your input image,

$$\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}$$

and you want to translate this image by 0.5 pixels in the positive horizontal direction using bicubic interpolation. These steps illustrate the bicubic interpolation algorithm followed by the block:

1. Zero pad the input matrix and translate it by 0.5 pixels to the right.

   

2. Create the output matrix by replacing each input pixel value with the weighted average of the two translated values on either side. The result is this matrix which has one column more than the input matrix:

   $$\begin{array}{cccc}0.375& 1.5& 3& 1.625\\ 1.875& 4.875& 6.375& 3.125\\ 3.375& 8.25& 9.75& 4.625\end{array}$$

Algorithms

Affine Transformation

The affine transformation matrix is a 3-by-2 matrix of form

$$H=\left[\begin{array}{cc}{h}_1& h_4\\ h_2& h_5\\ h_3& h_6\end{array}\right]$$

where h₁, h₂,...,h₆ are transformation coefficients.

The value of the pixel located at $$\left[x,y\right]$$ in the input image determines the value of the pixel located at $$\left[\widehat{x},\widehat{y}\right]$$ in the output transformed image. The relationship between the input and output point locations is defined by:

$$\{\begin{array}{c}\widehat{x}=x{h}_1+y{h}_2+h_3\\ \widehat{y}=x{h}_4+y{h}_5+h_6\end{array}$$

Projective Transformation

The projective transformation matrix is a 3-by-3 matrix of form

$$H=\left[\begin{array}{ccc}{h}_1& h_4& h_7\\ h_2& h_5& h_8\\ h_3& h_6& h_9\end{array}\right]$$

where h₁, h₂,...,h₉ are transformation coefficients.

The value of the pixel located at $$\left[x,y\right]$$ in the input image determines the value of the pixel located at $$\left[\widehat{x},\widehat{y}\right]$$ in the output transformed image.

The relationship between the input and output point locations is defined by:

$$\{\begin{array}{c}\widehat{x}=\frac{x{h}_1+y{h}_2+h_3}{x{h}_7+y{h}_8+h_9}\\ \widehat{y}=\frac{x{h}_4+y{h}_5+h_6}{x{h}_7+y{h}_8+h_9}\end{array}$$

The values of pixels in the output point locations are calculated using any of these interpolation methods: Nearest neighbor, bilinear, and bicubic interpolation.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2015b